Answer :
Let x represent the height of the model.
We have been given that a construction company built a scale model of a building. The model was built using a scale of 3 inches = 32 feet. We are asked to find the height of the model, if the building is expected to be 200 feet tall.
We will use proportions to solve our given problem as:
[tex]\frac{\text{Model height}}{\text{Actual height}}=\frac{\text{Model length}}{\text{Actual length}}[/tex]
Upon substituting our given values, we will get:
[tex]\frac{x}{200\text{ ft}}=\frac{3\text{ in}}{\text{32 ft}}[/tex]
[tex]\frac{x}{200\text{ ft}}\times 200\text{ ft}=\frac{3\text{ in}}{\text{32 ft}}\times 200\text{ ft}[/tex]
[tex]x=3\text{ in}\times 6.25[/tex]
[tex]x=18.75\text{ in}[/tex]
Therefore, the model will be 18.75 inches tall.